Mathematical Model to Formalize Tolerance Specifications and Enable Full 3D Tolerance Analysis

用于形式化公差规格并实现完整 3D 公差分析的数学模型

• 批准号: 0245422
• 负责人: Joseph Davidson
• 金额: --
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-05-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0245422&HistoricalAwards=false
• 关键词: Mathematical; Model; Formalize; Tolerance; Specifications

Tolerances specify the ranges of permissible imperfections so a manufactured part will be acceptable for assembly and use. Standards exist to define classes of tolerances and to ensure proper communication among engineers. The purpose of this research is to continue creating a mathematical model of geometric tolerances. The results from our earlier work show that the proposed math model is compatible with the standards, and that it provides three-dimensional relations for assemblies. At the local level, the method of the new model is to represent each tolerance-zone for a plane or a line as a hypothetical point-space, or map, and to combine these for assemblies of parts. At the global level, the model inter-relates all reference frames of an assembly using degrees of freedom. The project includes the implementation of a tolerance analysis system for comparison of the new model with existing software. Existing methods for analysing tolerances today are based strongly on ad-hoc conventions from engineering practice and less on mathematical principles. Consequently, full three-dimensional analysis of tolerances in assemblies is not done today, and contemporary design software is only partially compatible with existing standards. The outcome of this project will provide the tools to complete full three-dimensional statistical analyses of tolerances, and, thereby, it will improve quality and lower cost. This project will result in new teaching materials, which should make the subject easier to include in undergraduate and graduate engineering curricula. Based on our model, we are proposing to the American Standards Committee a new set of professional development classes and certification exams that are directed at engineers for tolerance analysis in the digital age.

公差指定了允许的缺陷范围，以便制造的零件可以组装和使用。 标准的存在是为了定义公差等级并确保工程师之间的正确沟通。 这项研究的目的是继续创建几何公差的数学模型。我们早期工作的结果表明，所提出的数学模型与标准兼容，并且它为装配体提供了三维关系。在局部层面，新模型的方法是将平面或直线的每个公差带表示为假设的点空间或地图，并将它们组合起来以进行零件装配。在全局级别，模型使用自由度将装配体的所有参考系相互关联。该项目包括实施公差分析系统，用于将新模型与现有软件进行比较。 当今分析公差的现有方法很大程度上基于工程实践中的临时约定，而不是基于数学原理。 因此，目前还没有对组件中的公差进行完整的三维分析，并且当代设计软件仅部分兼容现有标准。 该项目的成果将提供完成公差的完整三维统计分析的工具，从而提高质量并降低成本。 该项目将产生新的教材，这将使该主题更容易纳入本科生和研究生的工程课程。 根据我们的模型，我们向美国标准委员会提议一套新的专业发展课程和认证考试，针对数字时代的公差分析工程师。